In-vitro and in-vivo assessment of nirmatrelvir penetration into CSF, central nervous system cells, tissues, and peripheral blood mononuclear cells

Three years after SARS-CoV-2 emerged as a global infectious threat, the virus has become endemic. The neurological complications such as depression, anxiety, and other CNS complications after COVID-19 disease are increasing. The brain, and CSF have been shown as viral reservoirs for SARS-CoV-2, yielding a potential hypothesis for CNS effects. Thus, we investigated the CNS pharmacology of orally dosed nirmatrelvir/ritonavir (NMR/RTV). Using both an in vitro and an in vivo rodent model, we investigated CNS penetration and potential pharmacodynamic activity of NMR. Through pharmacokinetic modeling, we estimated the median CSF penetration of NMR to be low at 18.11% of plasma with very low accumulation in rodent brain tissue. Based on the multiples of the 90% maximal effective concentration (EC90) for SARS-CoV-2, NMR concentrations in the CSF and brain do not achieve an exposure level similar to that of plasma. A median of only 16% of all the predicted CSF concentrations in rats were > 3xEC90 (unadjusted for protein binding). This may have implications for viral persistence and neurologic post-acute sequelae of COVID-19 if increased NMR penetration in the CNS leads to decreased CNS viral loads and decreased CNS inflammation.


NMR PK exposures and percent (%) CSF penetration
The overall PK exposures for all rats are summarized in Table 2.The median (IQR) NMR penetration into the CSF was low at 18.1% (7.65-30.59)(calculated from highest predicted concentration [C max ]) and 15.2% (7.55-29.92)(calculated from area under the concentration-time curve [AUC]).The complete list of NMR penetration into CSF for each animal can be found in Table 2. Further, observed versus Bayesian predicted concentration time profiles for plasma and CSF vs. 90% maximal effective concentration [EC 90 ] and 3xEC 90 values can be found in Fig. 2. The CSF Bayesian prediction concentration time profiles for all animals showed the median (IQR) percent of time CSF concentrations were ≥ 3xEC 90 unadjusted for plasma protein binding (EC 90Un_adjusted, note: adjusted = EC 90Adjusted ) was 16% (0-20.5)(Fig. 2b).

Tissue and peripheral blood mononuclear cells (PBMC) NMR concentrations
The overall tissue accumulation ratio (AR [desirable AR: > 1]) and tissue concentrations for NMR can be found in Fig. 3 and Supplemental Fig. 3.The highest median (IQR) NMR tissue ARs were observed in the liver (2.71 [1.14-9.55]), and kidney (1.71 [0.82-11.09])while the lowest median NMR tissue AR was observed in brain tissue at 0.15 (0.03-1.12).Compared to all the tissues, the brain had the lowest median (23.83 ng/g, IQR: 10.94-46.85)NMR concentrations, which were all < 3xEC 90 regardless of adjustment for protein binding.For PBMCs, the median (IQR) value for the cellular AR for NMR was 0.998 (0.48-27.05).

Discussion
We found that NMR CSF concentrations in rats given oral NMR/RTV twice daily for five days were 15-18% of those in plasma, whether determined as a ratio of C max or AUC (Table 2).Further, we found that tissue penetration of NMR in brain of the rats was low, which was consistent with the NMR cell uptake in our in vitro model.Saleh and colleagues used physiologically based pharmacokinetic (PBPK) modelling to predict whether NMR, remdesivir, and molnupiravir achieve effective concentrations against SARS-CoV-2 in human brain cells 32 .Their model predicted NMR concentrations exceeded the EC 90 values in brain extracellular fluid concentrations, which is similar to what we found in rat CSF.However, they did not evaluate 3xEC 90 , or other multiplicative factors of the EC 90 values, reflecting levels of plasma exposure observed clinically.Exposure-response relationships for SARS-CoV-2 viral loads relative to EC 90 factors have not been evaluated in the CNS or other potential viral reservoirs.We utilized the concentration needed for 3xEC 90 for SARS-CoV-2 as our pharmacodynamic (PD) target for the CSF, based on the FDA review from EPIC-HR showing 95% of participants had NMR trough   .If the two EC 90 values utilized in the PBPK simulation study by Saleh and colleagues for the Delta variant are multiplied by a factor of 3 (0.149 µM: ~ 100 ng/mL × 3 = 300 ng/mL), the majority of time is spent below this PD goal.In our study, we found that CSF concentrations of NMR aren't maintained above the 3xEC 90Un_adjusted for SARS-CoV-2 (Fig. 2b, median overall CSF Concentrations ≥ 3 × EC 90 : 16%) for the entire dosing interval.As an exercise, we conducted Monte Carlo simulations (N = 1000, assuming 300 g rat, fraction unbound = 1) from the final rat population PK model to assess what doses (30-90 mg/kg) of NMR would be www.nature.com/scientificreports/required to achieve the probability of target attainment of 50-100% time above different EC 90 multiples (e.g., 0.5 − 3 × EC 90 ) in the CSF.Based on the simulations, doses of > 90 mg/kg BID (Supplemental Figs. 4 and 5) in rats would be necessary to ensure all concentrations are > 3 × EC 90Un_adjusted (i.e., 271.5 ng/mL).Humanizing this dose based on allometric scaling would result in clinical doses of 900 mg of NMR BID (three times the current FDA approved dose) or potentially more frequent dosing of 300 mg every 4 h.The simulations did not account for varying the doses of RTV (which increase NMR concentrations) given the toxicity and drug-drug interactions of RTV that make it clinically difficult to justify pushing its dose higher 35 .
Our study is unique as we also looked at homogenized liver, brain, lung, kidney, and heart tissues, and PBMC concentrations of NMR in rats.As shown in Fig. 3 and Supplemental Fig. 3, brain tissues had the lowest concentrations and AR compared with other tissues.Only rat 7, which died within 4 h after the 2nd dose, had NMR concentrations > EC 90Un_adjusted, but no rat had NMR concentrations > 3 × EC 90 regardless if comparing to adjusted or unadjusted for protein binding.For PBMCs, we found that intracellular NMR concentrations from PBMCs were detectable, and some rats had NMR PBMC concentrations above 3xEC 90Adjusted and Un_adjusted .When compared to other PIs used in the treatment of HIV, the desirable human PBMC cellular AR is > 1 36,37 .Our PBMC median (IQR) cellular AR for NMR was 0.998 (0.48-27.05) but the value demonstrated high variability among rats.Overall, it appears that NMR, in the presence of RTV, shows similar intracellular uptake to other PIs.This finding is important as previous studies have shown that SARs-CoV-2 can infect monocytes and T-lymphocytes 5,38 .
To evaluate specific drug uptake by relevant cells of the CNS rather than only CSF, we investigated the uptake of NMR and RTV in astrocytes, pericytes and neurons individually (Fig. 1).We found that the uptake of NMR and or RTV in the presence of the other drug differed significantly in neurons, astrocytes and pericytes.For neurons, the presence of RTV increased the uptake of NMR significantly.This increased uptake effect on NMR is likely a result of efflux transporter inhibition (p-glycoprotein [P-gp]) by RTV 39 .A study by Eng and colleagues looked at efflux transporter inhibition effects on NMR using Caco-2 cell monolayers 40 .They showed that inhibition of Breast Cancer Receptor Protein (BCRP) and Multi-Drug Resistance 1 (MDR1) enhanced the apparent permeability of NMR from 0.80 ± 0.15 to 4.05 ± 0.26 cm/s in Caco-2 cell monolayers 40 .Specific to CNS, a study by Ghosh and colleagues looked at cellular localization and functional significance of cytochrome P450 3A4 (CPY3A4) and MDR1 in the CNS and found coexpression by BBB endothelial cells and neurons showing Figure 3. Violin plots of tissue and PBMC AR for NMR.The highest median NMR tissue AR was observed in the liver and kidney, while the lowest median NMR tissue AR was observed in brain tissue.*Rat 7 only completed 1 day of treatment, no PMBC levels available.Rats 1 and 2 do not have lung or heart NMR concentrations due to tissue processing complications.# Calculated as a ratio of observed plasma NMR levels vs. tissue/PBMC levels at equivalent time of sampling.^Calculated using plasma level predictions vs. observed concentrations due to plasma NMR levels being BLOQ.AR accumulation ratio, BLOQ below level of quantification, IQR interquartile range.potential implications on drug metabolism and cytoprotective mechanisms 41 .As RTV is a substrate to many of the efflux transporters (relevant to the BBB), we predict similar effects of RTV on NMR permeability through the BBB 42 .The expression of P-gp in human brain capillary endothelial cells is well documented 43 .However, its expression in astrocyte, pericytes, and neurons is still under investigation [44][45][46][47] .No significant differences were noted in astrocytes and pericytes when NMR was administered alone or with RTV (Fig. 1a).More investigation is needed to further substantiate our hypothesis of the RTV-P-gp-NMR transporter interaction.Further studies by our group will evaluate NMR/RTV penetration utilizing a more novel 4-cell in vitro model, with transporter expression 48 .When comparing NMR to other PIs used to treat HIV, as a class, they achieve poor CSF exposure 49 .However, when co-administered with RTV (or other boosters), CSF penetration has been shown to increase 50,51 .For example, increased CSF concentrations of atazanavir were found when administered with RTV (7.9 to 10.3 ng/mL) 52 .When looking at RTV in our in vitro model, uptake by astrocytes was high at 41.97% and moderate by pericytes at 20.2%.In the presence of NMR, RTV uptake increased to 66.65% in astrocytes and 32.19% in pericytes.RTV CSF distribution is low [53][54][55] .To our knowledge, there are no prior studies for human neuronal uptake of RTV, and our results indicated moderate neuronal entry of RTV in the presence or absence of NMR (Fig. 1b).Nevertheless, a CNS drug delivery experiment for RTV in a mouse model showed moderate penetration of RTV in brain parenchyma tissue 56 .Additional characterization of RTV uptake for human neuronal tissue is desired.A study by Anthonypillai and colleagues in guinea pigs found that CSF levels of RTV were low, but RTV levels in the choroid plexus and brain were higher 53 .They hypothesized this was due to RTV regulation in the CSF and choroid plexus by efflux transporters that may limit drug accumulation in the CSF.In our study, we found that RTV uptake in astrocytes and pericytes was affected by NMR (Fig. 1b).Thus, we believe this is likely due to NMR's effect on associated transporters.Transporter inhibition studies are warranted to provide insight on the mechanisms behind the differences seen between cell lines.It is relevant to note the BCSFB is considered "leakier" compared to the BBB and transport across is inversely related to molecular weight of the compound.This is due to the BCSFB being comprised of ependymal cells of the choroid plexus.This results in looser tight junctions compared to those found in the BBB.As such, drug penetration into the CSF is not an index of BBB transport, but rather a measure of transport across the choroid plexus at the BCSFB.
We developed a 3-compartment PK model to predict individual animal concentration-time profiles for plasma and CSF, as shown in Fig. 2.This allowed us to accurately predict CSF and plasma exposures, which were used to calculate CSF penetration (Table 2).This also allowed us to make comparisons of our PK estimates with clinical and animal data.For example, the median half-life for NMR in the presence of RTV for the rats was 2.4 × faster than what is seen in humans (2.55 h vs. 6.05 h) 9 .This is expected as smaller animals clear most drugs faster given the principles of allometry 40,57 .When comparing our NMR half-life to other animal models for NMR, we found that our half-life estimation was within the range of other oral rat PK studies (10 mg/kg: 4 h [range: 2.9-5.1], 10 mg/kg: 2.8 h ± 1.4 h) 40,58 .Our estimation for time at which C max is first observed (T max ), was similar to other rodent models (mean: 1.84 h vs. mean: 1.5 h) 40,58 .The median relative F value of 54.5% in our study was also consistent with other literature values estimated in rats for NMR (34-50%) 40 .We note our animals were not restricted of food or water, and this is likely why we saw variability in F between and within animals (Table 1b: range: 32-62%).For NMR Ka, our model estimate of 0.51 h −1 was also in agreement with finding reported by others (0.55 h −1 ) 34 .We compared our values for C max and AUC with clinical data from healthy volunteers.Rat geometric mean plasma values for C max (2.48 µg/mL or 2480 ng/mL) and AUC daily average (20.25 µg*hr/mL) compared well with healthy human geometric mean values of C max (2.21 µg/mL) and AUC 0-12 h (23.01 µg*h/mL) supporting our allometric dose scaling strategies 34 .Our AUC estimation was a daily average given the difficulty of standardizing twice-daily dosing in animals and the healthy volunteer data was based on an AUC of 0-12 h.When comparing our rat CSF concentrations to the PBPK modeling performed by Saleh and colleagues, our CSF C max (median 0.41 mg/L or 410 ng/mL) is in agreement with what was projected in human brain extracellular fluid (~ 0.3-0.44 mg/L, points extrapolated using graphgrabber 2.02) 32,59 .This shows the potential clinical application of our rat model as we were able to humanize C max exposure in both plasma and CSF.Last, it is important to also mention NMR's lipophilicity in relation to BBB penetration.A drug metabolism study on NMR disposition indicated that it is moderately lipophilic with a lipophilicity coefficient (LogP) of 1.68, showing low passive apparent permeability (P app ) of 1.76 × 10 −6 cm/s 40 .Utilizing different cell lines (i.e., Caco-2 cell monolayers), NMR exhibited similar trends of low permeability across the monolayer barrier 40 .Our findings of low penetration of NMR through the BBB are also in agreement with Lipinski's rule of five that postulates a lipophilicity range of 2.0 to 3.5 is a fundamental predictor for BBB penetration via passive diffusion 60 .Other PIs exhibit a range of lipophilicity from 1.0 to 5.69 depending on specific physiochemical properties 61,62 .
Our study has limitations.First, we did not design this study for animals infected with SARS-CoV-2 and thus could not assess viral loads in the CSF vs. CSF concentrations of NMR.Because our findings indicate that CNS levels of NMR may not be adequate to achieve therapeutic concentrations, plans for utilizing an infection model with the golden Syrian hamster model are ongoing.Second, our tissue concentrations represent total drug concentrations based on homogenized tissues.Understanding the dynamic relationship of unbound tissue concentrations vs. time or site-specific tissue concentrations would require microdialysis or other techniques.Further, it is unknown if CSF catheter placement could have influenced CSF penetration or if concentrationmediated changes to CSF transit occur.Future work to address concentration-mediated penetration utilizing a BCSFB in vitro model is planned 48 .In addition, it is unclear how our animal model compares to active infection where inflammation could increase drug penetration through the BBB in active SARs-CoV-2 infection.In this context, a recent review on BBB integrity alteration by SARs-CoV-2 pointed to the increased expression of matrix metalloproteinase-9 (MMP9) in COVID-19 infection.The increased MMP9 activates RhoA (Ras homolog family member A), causing more degradation of type IV collagen of the BBB basement membrane and altering the barrier's integrity 63 .Moreover, in our in vitro experiment for cellular uptake of NMR/RTV by human brain cells, we did not include human brain microvascular endothelial cells (hBMECs) because our earlier finding suggested no infection of hBMECs by SARs-CoV-2, while we observed high infection in human astrocytes and pericytes 18 .This was consistent with the lack of ACE-2 receptor expression in hBMECs, when compared to astrocytes and astrocytes.Additionally, the cells were not available at the time of these experiments.Differences in the expression of BBB transporters (i.e., P-gp) among species exist, and variations could result in differences in clinical extrapolation.A study by Morris and colleagues showed cross species expression of BBB transporters and that rats and humans have many of the same transporters present 64 .However, describing species differences in transporter expression is a difficult task given all the potential transporters involved with NMR and RTV and was beyond the scope of this study.A mechanistic study by Verscheijden and colleagues used PBPK modelling and calculated plasma concentration-corrected brain concentrations (Kp) values for humans and rodents specific only for P-gp correction for various medications 65 .We acknowledge the complexity of the BBB transporter expression between species.However, regardless of transporter differences, our dosing achieved humanized exposures in plasma and CSF.Further studies specific to transporter expression are warranted and planned.Also, we quantified total NMR concentrations and did not quantify free drug (NMR is 69% protein bound) 9 .CSF penetration via plasma to CSF estimation should also consider free drug in the plasma as drug found in the CSF is unbound to proteins, and future studies might quantify free NMR concentrations to capture this consideration more accurately.The PD endpoints we utilized for CSF, plasma, tissues, and PBMC were adjusted and unadjusted for plasma protein-binding, depending on the matrix.Last, our final model estimation of K 30 denotes overall elimination of NMR from the CSF, including uptake by various types of cells in the CNS.This may be an oversimplification and a more mechanistic description should be evaluated utilizing an advanced quantitative systems pharmacology approach.
In this study, we determined NMR CSF and CNS penetration utilizing in vitro and in vivo models and quantitatively described the transit of NMR from plasma to the CSF.In addition to NMR, molnupiravir and remdesivir are two other antiviral agents for the treatment of SARS-CoV-2.Similarly, CNS penetration data for them are lacking.The data from our in vivo rat model demonstrates that NMR penetration into CSF and CNS tissues may be inadequate.Our in vitro model data shows minimal NMR uptake into cells relevant to the CNS.Collectively, these findings may have implications for viral persistence in these compartments and neurologic post-acute sequelae of COVID-19.These data motivate future investigations utilizing an infection model to understand the pharmacodynamic effects of NMR drug concentrations in the CNS on viral loads in the CNS.If longer treatment or higher doses correspond to increased NMR penetration in the CNS, decreased viral loads, and decreased CNS inflammation, they provide a basis to investigate alternative dosing strategies.This information would be fundamental for optimizing treatment of Long COVID-19.

Methods
This study was conducted at the University of Nebraska Medical Center in Omaha, NE.All study methods were approved by the Institutional Animal Care and Use Committee (IACUC; Protocol #2006507) and conducted in an AAALAC-accredited animal facility.This study was reported in accordance with ARRIVE guidelines.

Cell seeding in 6-well plates
All steps were carried out in a biosafety cabinet under aseptic conditions, similar to methods previously described 48 .Astrocytes with a cell count of 0.5 × 10 6 /well were seeded into 6-well plates containing 2 ml of astrocyte media in each well.Seeding was performed in triplicate for each drug or drug combination and incubated in 37 °C cell culture incubator, as described in our previous work 48 .Pericytes with a cell count of 0.5 × 10 6 /well were seeded into 6-well plates containing 2 ml of pericyte media in each well.Cell seeding was performed in triplicate for each drug or drug combination and incubated in 37 °C cell culture incubator.Neurons with a cell count of 0.3 × 10 6 /well were seeded into 6-well plates containing 2 ml of neuronal media in each well.Seeding was performed in triplicates for each drug or drug combination and incubated in 37 °C cell culture incubator.

Drug formulation for in-vitro work
Powdered NMR (Medkoo Biosciences, Catalog#555985, Lot#: C22R06B23) was dissolved in 1 mL of 100% DMSO to make a stock concentration of 4.4 mg/mL.Powdered RTV (Medkoo Biosciences, Catalog#318671, Lot#: A22M08B04) was dissolved in 1 mL of 100% DMSO to achieve the stock concentration of 2 mg/mL.NMR and RTV were weighed and dissolved in 1 mL of 100% DMSO to achieve 4.4 and 2 mg/mL stock concentration for NMR and RTV, respectively.

Drug addition to cells and sample preparation
NMR and RTV, individually or in combination, were added to the cultured cells at 2200 ng/mL and 1000 ng/ mL final concentration, respectively.The in vitro doses of NMR and RTV were selected based on previous studies 67,68 .After 24-h incubation with drugs, astrocytes, pericytes, and neuron cells were washed once with PBS and harvested using a cell scraper (Corning #3010) in 500 µl of 70% methanol.Samples were kept at − 20 °C prior to drug quantification.

Experimental design and animals
Male Sprague-Dawley rats (n=10, mean weight=306 g, age=~65-70 days) were obtained from Charles River (Raleigh, NC 27610).All catheters (cisternal and vein cannulation) for the animals were surgically implanted 69,70 at Charles River prior to shipping.On arrival to the housing facility, animals were acclimated for 72 hrs prior to starting study protocol.Catheter management was performed daily to ensure viable sampling.Animals were administered 30 mg/kg NMR + 10 mg/kg RTV twice a day (60 mg/kg NMR and 20 mg/kg RTV total daily dose) daily for five days (as described below).All NMR/RTV doses were administered orally via gavage.The dose chosen for this study was allometrically scaled to a humanized equivalent of NMR/RTV based on fixed dosing (i.e., 60 kg patient, 300 mg NMR + 100 mg RTV twice daily, = 10 mg/kg NMR + 3.33 mg/kg RTV daily x scaling factor of 6.2 = ~60 mg/kg NMR + ~20 mg/kg RTV daily) 57 .The five day duration of the study also aligns with the current FDA recommendation for treatment of COVID-19 with NMR/RTV in patients 10 .Rats were housed in a light and temperature-controlled room for the duration of the study and allowed free access to water and food, except during sampling.Data were analyzed for all animals that entered the protocol.When animals contributed incomplete data (i.e., early protocol termination), all available samples were analyzed for PK.Concentrations below the lower limit of quantification were inputted as 0 71 .

Blood, CSF, PBMC, and tissue sampling and determination of NMR concentrations
Blood samples were drawn from a single right-sided internal jugular vein catheter in a sedation-free manner when possible.Blood catheter lines were flushed with normal saline after each blood draw to prevent blood contamination.CSF was collected via an intracisternal catheter.Isoflurane gas was used for temporary sedation when needed (5% initially, followed by 1-3% maintenance).Within each 24 hrs, planned sample collection was eight blood and two CSF samples per animal.An approximation of the full sampling strategy over the five day study can be found in Supplemental Fig. 6.Each sample obtained (0.25 mL blood and 0.05-0.1 mL CSF aliquots) was replaced with either an equivalent volume of normal saline or artificial CSF (as appropriate) to maintain euvolemia.Blood and CSF samples from NMR-treated animals were processed similar to our previous reports [72][73][74][75] .Upon completion of the protocol, rats were euthanized, and tissues (lungs, heart, kidney, brain, liver) were harvested.The tissues were perfused, rinsed with cold saline solution, blotted with paper towel, and snap-frozen.Rat tissues (lungs, heart, kidney, brain, liver) were analyzed for NMR content by preparing tissue homogenate samples.PBMC sampling was conducted on each rat prior to termination using mononuclear cell preparation tubes per manufacture protocol (BD Biosciences, Franklin Lakes, NJ).
Plasma, CSF, tissue, and PBMC concentrations of NMR were quantified with LC-MS/MS using individual standard curves for each matrix (ranges: CSF, 1-250 ng/mL; plasma, 20-10,0000 ng/mL; PBMC, 0.01-5 ng/mL).Standard calibrators, quality controls, and samples were prepared in microcentrifuge tubes.Internal standard was added to track the analyte of interest through the extraction and instrumentation processes.NMR was extracted from 20 μL of rat plasma, PBMCs or CSF with a stable labeled internal standard [2H9]-PF-07321332 (IS) by a protein precipitation using 50:50 ACN:MeOH to provide a protein free extract.CSF samples were treated with ammoniated methanol prior to extraction to ensure no analyte adsorbs to the tube wall as previously described 74 .Supernatant was removed and diluted with mobile phase in a 96-well plate prior to injection.HPLC was used to separate the analytes from potential interferences on a C18 100 × 3.00 mm column (MAC MOD, Chadds Ford, PA, USA) for stationary phase, using 60% acetonitrile, 0.1% formic acid in water as an isocratic mobile phase.Detection of NMR and the IS in plasma and CSF was done with an ABSciex 5500 Q-trap mass spectrometer (ABSciex, Framingham, MA, USA) in positive ion mode.PBMC levels were converted to µM concentrations based on the single cell volume for PMBCs 76 .The assays were linear between plasma concentrations of 20 and 10,000 ng/mL, CSF concentrations of 1 and 250 ng/mL, and PBMC concentrations of 0.01 and 5 ng/mL.The plasma component underwent a complete validation and had a precision of < 4.73 for all measurements, including intra-and inter-assay measurements.Briefly, all bioanalyses were within the pre-determined acceptance criteria of +/− 15% for each level (+/− 20% for LLOQ) 77 .
Tissues were homogenized using a Precellys Evolution Cryolys homogenizer (Bertin Technologies, Montignyle-Bretonneux, France).Each tissue was homogenized with 0.5 mL of 70:30 methanol: 25 mM phosphate buffer.Calibration curves for the tissue homogenates were prepared as described above in the section on estimation of NMR in plasma.Tissues were quantified by weight (mg of drug/g of tissues), reported as mg/g, and converted to mg/mL as previously described 72,78 .Calibration curves for the tissue homogenates were prepared as described above.All units were reported in ng.
PBMC cellular and tissue AR were calculated as observed NMR PBMC and tissue concentrations to NMR plasma concentrations at the same time of collection 36,37 .

NMR PK and drug exposure
The simplest base PK model considered was a 3-compartment model with an oral compartment (first order absorption), plasma compartment, and a CSF compartment.Three and four-compartment models with/without a lag constant were similarly fit using the nonparametric adaptive grid (NPAG) algorithm within the Pmetrics package version 1.5.0 (Los Angeles, CA) for R version 3.2.1 (R Foundation for Statistical Computing, Vienna, Austria) 79,80 .Multiple different CSF models were considered where CSF intercompartmental clearance (CL)/ transfer and CSF CL were added and omitted based on investigator judgement, and other PK CSF studies [81][82][83][84] .A model comparison table can be found in Supplemental Table 1.The initial estimate of parameter weighting was accomplished using the inverse of the assay variance.Model performance was quantitatively described using observed vs. predicted concentrations to calculate bias, imprecision, and coefficients of determination 85 .The final model was selected based on regression of observed vs. predicted concentrations, prediction bias, visual plots of parameter estimates, lowest -2LL/Akaike information criterion and rule of parsimony.We modeled the relative bioavailability (F) for each dose in a given rat to account for inter-occasion variability in concentrations among doses, by taking the maximum post-dose peak concentration observed for that rat over all doses and calculating F for each dose as the peak after that dose divided by the maximum peak.The dose which was followed by the maximum peak then had F=1, and all other doses were F≤1.
To compare NMR concentrations in animals to a putative PD endpoint, the concentration needed for three times the 90% maximal effective concentration (3xEC 90 ) for the SARS-CoV-2 was utilized 33 .The FDA integrated review from the clinical studies (EPIC-HR) showed 95% of participants had NMR trough concentrations ≥3xEC 90 34 .Therefore, the goal for the CSF was set to achieve the same exposure conditions as for plasma.The plasma EC 90Adjusted concentration for plasma is 292 ng/mL (585 nM), and the EC 90Un_adjusted for CSF is 90.5 ng/ mL.Therefore, the 3xEC 90 PD values would be 876 ng/mL for plasma and tissue, and 271.5 ng/mL for CSF.This EC 90 value is based on the study on bronchial epithelial cells infected with USA_WAI/2020 isolate 58 .

Estimation of PK exposure and percent (%) CSF penetration
The best-fit model was used to calculate median maximum a posteriori probability Bayesian NMR plasma and CSF concentration estimates at 12-min intervals over the 5-day study period using each animal's measured NMR concentrations, exact dose, and dosing schedule.From these concentrations we calculated the AUC_ 0-5 days over the entire experiment using "makeAUC" function within Pmetrics 79,86 .C max_0-5 days from the 12-min interval Bayesian estimates was determined to be each animal's C max_0-5 days .
Ratios of the estimated AUC csf /AUC plasma and C max _ csf /C max _ plasma were used to determine percent CSF penetration 81,[87][88][89][90] .AUC was standardized to AUC 0-24 h by dividing AUC_ 0-5 days by 5 (i.e., 5-days protocol) to provide an estimated AUC 0-24 h value.For C max _ 0-5 days, the highest predicted CSF concentration and corresponding plasma concentration were used to calculate precent penetration.Only animals with CSF concentrations sampled were used for estimation of CSF penetration.

Statistical methods
Summary statistics were calculated using GraphPad Prism V7.02 (GraphPad Software Inc., La Jolla, CA).Nonparametric summary statistics were reported given the small sample size and distribution of data.

Table 1 .
Median parameter values from final model (a) and individual animal NMR half-life and average bioavailability (b).PK pharmacokinetic, CV% coefficient of variation percent, CL NMR clearance, V c volume central compartment, V csf volume cerebrospinal fluid compartment, K 23 rate constant to cerebrospinal fluid from central compartment, K 30 elimination rate constant from CSF compartment, IQR interquartile range, T max time at which C max was first observed.*Bioavailability was estimated after each dose given the variability of oral absorption, as described in Methods.**Rat 7 only completed 1 day of treatment.# Calculated to compare to literature values.^ Estimation to assess if the data are insufficient to precisely estimate the individual parameters.$ Estimation denotes overall elimination of NMR from the CSF, including uptake by various types of cells in the CNS.

Table 2 .
NMR plasma and CSF PK exposures estimated using Bayesian posteriors for AUC 0-endoftreatment and C max _ 0-5 days and percent penetration of NMR into the CSF compared to blood.Units for C max converted to ng/ mL for consistency.AUC kept in µg*hr/mL.C max maximum concentration, AUC area under the curve, CSF cerebral spinal fluid, T ½ half = life, IQR interquartile range, SD standard deviation.*Excludingrat 7 as noCSF was obtained from this animal, #Calculated to compare to clinical data.Animal C